2018\19 Ratings Calculations

So How Did I Get That Rating?

For rating purposes, new, unrated players
are assumed to have an initial rating of 1300 based on zero previous
games.

The rating calculation formulas
are modified versions of the old USCF ratings formulas. There are two
main calculation formulas: provisional,
for players who have played fewer than 20 rated BAL games at the start
of the rating cycle, and established,
for those who have played 20 or more rated BAL games at the start of
the rating cycle.

Within a rating cycle, performance ratings are first calculated for all
new, unrated players. These performance ratings are then used when
calculating the ratings of the remaining players.

Provisional Ratings Calculation

The provisional rating calculation formula is:

(np × Rp) + ( ∑ Ro
) + (400
× (
∑ W - ∑ L))

G =

np
+ nc

-
Rp

where

G is
the gain in rating (can be negative),

np
is the number of games
played prior to the ratings cycle,
Rp is the player's previous rating,
∑ Ro is the sum of the ratings of the
player's
opponents,
∑ W is the sum of the player's wins (win = 1, draw = 0.5),
∑ L is the sum of the player's losses (loss = 1, draw = 0.5), and
nc is the number of games played in this
ratings cycle

Established Ratings Calculation

The established rating calculation is a bit more complex:

G =

k
× (
∑W
- ∑We )

where

G
is the gain in rating (can be negative),
k is a constant based on the player's previous rating (16 if over 2399,
24 if between 2100 and 2399, and 32 otherwise),
∑W is the sum of the player's game scores (win = 1, loss = 0, draw =
0.5), and
∑We is the sum of the player's "expected wins"
against each
opponent, computed for each opponent as:

1

We=

1 + 10 -
(Δr ÷
400)

where Δr is the difference
between the
player's and opponent's rating.

K-Adjustment

After the appropriate calculation is performed, the resulting
gain may be adjusted if the player's new rating crosses one of the "k"
boundaries as follows ( RO = old rating, RN= new rating):If
(either RO or RN) >
2099

If
((both RO and RN) ≥ 2400) OR (2100 ≤ (both RO and RN) ≤ 2400)

RN
is not changed

ElseIf (RO <
2100)

RN
= 2100 + (RN - 2100) × 0.75

ElseIf RO <
2400

If
RN < 2100

RN
= 2100 + (RN - 2100) × 1.33

ElseIf RN >
2399

RN
= 2400 + (RN - 2400) × 0.66

Else

RN
is not changed

ElseIf RO ≥ 2400

If
RN < 2400

RN = 2400 + (RN - 2400) ×
1.50

Else

RN
is not changed

Else

RN
is not changed

Rounding

Finally, if the change is less than 1, the new rating is rounded up (to the next highest integer) if G is positive, or
rounded down (to
the next lower integer) if G
is negative. This ensures that a positive result will mean the gain of
at least one point, and a negative result will mean the loss of at
least one point.